Physically unclonable functions with enhanced margin testing

ABSTRACT

Apparatus for identifying stable physically unclonable function (PUF) cells includes an array of PUF cells, a bias control circuit, and a selector circuit. The bias control circuit has a plurality of bias control lines that apply one or more bias control signals to each PUF cell in the array of PUF cells. The selector circuit selects a subset of the PUF cells in the array of PUF cells based on whether outputs of the PUF cells in the array of PUF cells change in response to application of the bias control signals. A corresponding method is also disclosed.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to provisional patent application No.61/940,076, filed Feb. 14, 2014, which is hereby incorporated byreference in its entirety.

FIELD

The present disclosure relates to a method and an apparatus forenhancing the stability of physically unclonable functions.

BACKGROUND

A Physically Unclonable Function (PUF) is a physical circuit inside anintegrated circuit device whose behavior is determined by randomphysical variations inside the integrated circuit or within theproximate environment of the integrated circuit. PUFs may be used toderive encryption keys for configuring Programmable Logic Devices (PLDs)such as Field Programmable Gate Arrays (FPGAs), which are integratedcircuits that include programmable logic blocks and programmablerouting. The random physical variations in and around the integratedcircuits may be due to random manufacturing variations within the device(such as variations in transistor thresholds, transistor driverstrengths, capacitances, or resistances), or may be due to explicitlyadded sources of variations (such as device coatings that contain aslurry of dielectric particles that cause random fluctuations incapacitance sensors).

Because of these variations, corresponding PUFs on multiple ostensiblyidentical devices will behave differently. Sometimes, a PUF will acceptan input (called a challenge), and produce an output (called aresponse). A response may include multiple bits. Alternatively, a PUFmay return a response with no need for an explicit challenge. The randomvariations between ostensibly identical devices may cause thecorresponding PUFs in different devices to return different responsesunder the same conditions (including in response to the samechallenges).

PUF responses may be used to create, encrypt, or obfuscate encryptionkeys. The PUF responses can also be used to create unique ID values thatcan be used to uniquely identify a device, or to otherwise make onedevice behave differently from another ostensibly identical device.These use cases require, for a particular instance of a device, that thePUF response for a particular challenge input be stable (such that itconsistently returns the same value for that challenge on that device).

SUMMARY

The present disclosure provides systems and methods for improving thestability of PUFs. In one embodiment, an apparatus is provided foridentifying stable physically unclonable function (PUF) cells. Theapparatus includes an array of PUF cells, a bias control circuit, and aselector circuit. The bias control circuit has a plurality of biascontrol lines, which apply one or more bias control signals to each PUFcell in the array of PUF cells. The selector circuit selects a subset ofthe PUF cells in the array of PUF cells based on whether outputs of thePUF cells in the array of PUF cells change in response to application ofthe bias control signals.

The bias control circuit may include at least one capacitor coupling anode of a PUF cell in the array of PUF cells and one of the one or morebias control signals. Each PUF cell in the array of PUF cells may bebased on a voltage and may be a butterfly PUF cell or a SRAM PUF cell.

The bias control circuit may include at least a transistor connected toa load capacitor such that when the transistor is disabled, the loadcapacitor is disconnected from a delay path for a PUF cell in the arrayof PUF cells. Each PUF cell in the array of PUF cells may be based on adelay and may be an arbiter PUF cell or a ring oscillator PUF cell.

The apparatus may further include a polarity control circuit thatselectively changes a polarity of at least one bias control signalbefore the one or more bias control signals are applied to each PUF cellin the array of PUF cells. The polarity control circuit may selectivelychange the polarity based on a nominal response of the PUF cells.

A first PUF cell that has a changed output when the one or more biascontrol signals are applied to the first PUF cell may be less stablethan a second PUF cell that has an unchanged output when the one or morebias control signals are applied to the second PUF cell. The selectorcircuit may select the subset of PUF cells by selecting a predeterminednumber of PUF cells in the array of PUF cells that are more stable thana remainder of the PUF cells in the array of PUF cells.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features of the invention, its nature and various advantageswill be apparent upon consideration of the following detaileddescription, taken in conjunction with the accompanying drawings, inwhich like reference characters refer to like parts throughout, and inwhich:

FIG. 1 shows an illustrative block diagram of a delay-based arbiter PUF,in accordance with the prior art;

FIG. 2 shows an illustrative block diagram of a delay-based ringoscillator PUF, in accordance with the prior art;

FIG. 3 shows an illustrative block diagram of a balanced butterfly PUF,in accordance with some embodiments of the present disclosure;

FIG. 4 shows an illustrative block diagram of a logic-based butterflyPUF, in accordance with some embodiments of the present disclosure;

FIG. 5 shows an illustrative block diagram of a balanced SRAM PUF, inaccordance with some embodiments of the present disclosure;

FIG. 6 shows an illustrative block diagram of a matrix of SRAM bitcells, in accordance with the prior art;

FIG. 7 shows an illustrative block diagram of a balanced PUF bit cell,in accordance with some embodiments of the present disclosure;

FIG. 8 shows an illustrative block diagram of a bias control circuit fora balanced PUF bit cell, in accordance with some embodiments of thepresent disclosure;

FIG. 9 shows an illustrative block diagram of a bias control circuit anda polarity control block for a balanced PUF bit cell, in accordance withsome embodiments of the present disclosure;

FIG. 10 shows an illustrative graph of various voltage levels at a biascontrol circuit and a PUF bit cell, in accordance with some embodimentsof the present disclosure;

FIG. 11 shows an illustrative block diagram of a bias control circuitfor a delay-based PUF bit cell, in accordance with some embodiments ofthe present disclosure; and

FIG. 12 shows an illustrative flow diagram of a process for improvingthe stability of an array of PUF cells, in accordance with someembodiments of the present disclosure.

DETAILED DESCRIPTION

To provide an overall understanding of the invention, certainillustrative embodiments will now be described. However, it will beunderstood by one of ordinary skill in the art that the systems andmethods described herein may be adapted and modified as is appropriatefor the application being addressed and that the systems and methodsdescribed herein may be employed in other suitable applications, andthat such other additions and modifications will not depart from thescope hereof.

The figures described herein show illustrative embodiments, however thefigures may not necessarily show and may not be intended to show theexact layout of the hardware components contained in the embodiments.The figures are provided merely to illustrate the high level conceptuallayouts of the embodiments. The embodiments disclosed herein may beimplemented with any suitable number of components and any suitablelayout of components in accordance with principles known in the art.

A response of a PUF on a device for a particular challenge input shouldbe stable, so that the response of the PUF consistently returns the samevalue for that particular challenge. However, random variations in oraround the device on which the PUF response depends may vary over time.These variations may be due to changes in operating temperature oroperating voltage, stress-related changes in transistor characteristicdue to Negative Bias Threshold Instability (NBTI), Positive BiasThreshold Instability (PBTI), or accumulated environmental radiationeffects, or simply to thermal noise. The variations can cause theresponse of the PUF to change, or “flip”. As used herein, “flip” refersto a change in PUF response and is an indication of instability. As anexample, a PUF bit cell may provide a PUF response of a ‘0’ or a ‘1’value under certain conditions. When those conditions change (due to anyof the random variations described above, for example), the PUF responsesometimes flips, meaning that the PUF response that was originally a ‘0’has changed to a ‘1’ or the PUF response that was originally a ‘1’ haschanged to a ‘0’. Most of the present disclosure is described withrespect to PUF bit cells exhibiting flipping behavior as an indicationof instability. However, in general, one of ordinary skill in the artwill understand that the present disclosure is also applicable tosystems in which a PUF response may take on non-binary values, andchanges in those non-binary values are indications of instability.

As an example, SRAM cells, such as the SRAM cell shown in FIG. 5, oftenpower up to an unknown state in a random pattern. Depending on thevarious strengths of the transistors in the SRAM cell, an SRAM cell maypower up to a ‘0’ or a ‘1’ value. The various strengths of thetransistors arise from random manufacturing variations that may varyfrom transistor to transistor that cause the transistors to havedifferent threshold voltages. Moreover, the threshold voltages may varywith age of the device. These variations may cause instability in PUFbit cells, which causes PUF responses to be unpredictable. The presentdisclosure describes systems and methods for increasing the stability ofPUFs.

Examples of PUFS include arbiter PUFs, ring-oscillator PUFs, butterflyPUFs, and SRAM PUFs. One technique for stabilizing such PUFs is to reada PUF response multiple times, and, for each response bit, use the valueof that bit that occurs most often (this is referred to as “majorityvoting”). One problem with majority voting is that it is only effectivefor averaging away truly random fluctuations—such as those due tothermal noise, and cannot correct consistent changes in variation due tofactors such as aging and stress.

Another technique for stabilizing PUFs makes use of additionalnon-volatile “helper-data”. PUF implementations use helper-data byreading a first set of one or more responses for a given challengeinput, generating a non-volatile helper that will aid in the re-creationof future responses for the challenge input, and then saving the helperdata in (possibly public) non-volatile storage. This may be referred toas the “recruitment phase”. In one example, helper-data may be used inError Correcting Codes (ECC), where the helper data may include anerror-correction syndrome for the response. However, one problem withusing ECC is that the syndrome reveals some information about the PUFresponse, which becomes especially problematic when the number of bitsin the syndrome approaches the number of bits of entropy in the PUFresponse. Thus, using helper-data in ECC is particularly undesirablewhen the PUF response is used to create encryption keys that should bekept secret.

In another example, helper-data may be used to select a subset of PUFresponse bits which appear to be the most stable, and mask out thoseresponse bits that do not appear to be stable. This may be performedduring the recruitment phase by reading the PUF response multiple timesand counting how many times a particular PUF response bit is a 0 or 1.One problem with this technique is that it can only detect marginalresponse bits whose margin is on the order of the thermal noise. Forexample, if the source of variation for a PUF is due to variations intransistor threshold voltages (which is a major source of variation formany PUFs), and the standard deviation in the threshold voltage is 30mV, about half of the PUF bits would have a margin of above 30 mV, butsome of the PUF response bits may have a lower margin such as equal toor less than 6 mV. If the thermal noise were 1 mV, only PUF responsebits whose margin was on the order of 2-3 mV may be detected using thistechnique. However, it is more challenging to test the stability of PUFcells with margins that are higher than a small multiple of the thermalnoise, because these cells would tend to exhibit stable behavior. Thesystems and methods of the present disclosure improve upon thesetechniques by enhancing the ability to check the margin of each responsebit.

One way to enhance the margin testing of a response bit is to apply oneor more bias control lines to a PUF bit cell. Although some of thefigures of the present disclosure may indicate specific numbers of biascontrol lines used in some of the illustrative embodiments, thosenumbers of bias control lines may be provided by way of example only.The embodiments disclosed herein may be implemented to accommodate anysuitable number of bias control lines.

The bias control lines form an assertion pattern (a pattern of zeros andones, for example) that may be applied to an array of PUF bit cells,where each PUF bit cell corresponds to one response bit. As used herein,an assertion pattern that gives rise to approximately an equal number of0 and 1 response bit values may be referred to as a nominal bias settingof the bias control lines. The resulting bias may be referred to hereinas the nominal bias. In contrast, an assertion pattern that on average,causes more than half of the response bits to be read as a 1 may bereferred to as a positive bias setting. An assertion pattern that onaverage, causes more than half of the response bits to be read as a 0may be referred to as a negative bias setting.

In accordance with some embodiments of the present disclosure, duringthe recruitment phase, a PUF response is initially read under nominalbias. Multiple reads may be additionally performed to obtain further PUFresponses, and majority voting on each bit may be performed to computethe most common response for each bit. After the nominal response foreach PUF bit is determined, the bias control signals may be used tomeasure the stability of each response bit.

The systems and methods of the present disclosure may be described indetail with reference to FIGS. 1-12. More particularly, FIGS. 1, 2, and6 show block diagrams of known implementations of various PUFs and SRAMbit cells in accordance with the prior art. Various implementations ofPUF cells in accordance with the present disclosure are described withreference to FIGS. 3-5 and 7-9. A graphical example of an effect of biascontrol signals on complementary nodes in a PUF cell is shown in FIG.10, and a delay-based PUF cell, in accordance with the presentdisclosure, is described with reference to FIG. 11. A flow diagram of amethod for enhancing the stability of a PUF cell, in accordance withsome embodiments of the present disclosure, is shown in FIG. 12.

PUFs may be implemented based on voltages or delays. In particular,depending on the particular PUF implementation, the systems and methodsof the present disclosure may use different circuitry for enhancing thestability of the PUF bit. Some balanced PUFs, such as butterfly PUFsshown in FIGS. 3 and 4 and SRAM PUFs shown in FIGS. 5 and 6, stronglydepend on the initial voltages of a pair of complementary nodes. Often,the initial voltage variations on these nodes may be as significant, andin some cases indistinguishable, from the underlying variations thatthat the PUF is attempting to measure (such as the threshold voltage ofa transistor).

In such cases, the systems and methods of the present disclosure mayinclude one or more capacitors coupled to each of the complementarynodes such that the voltage level on a bias control line is coupled toone of complementary nodes through one of those capacitors, as is shownin FIGS. 8 and 9 in accordance with some embodiments of the presentdisclosure. Capacitors feeding the complementary nodes are coupled todifferent bias control lines, such that changing the voltage on the biascontrol line may change the voltage on the complementary node. Inparticular, a voltage change on a control line may be coupled throughthe connected capacitor to one of the complementary nodes. If the valueof the coupling capacitor is equal to 1/X of the value of the overallcapacitance on the complementary node from all sources, then the voltagedifferential coupled onto the complementary node may be equal to 1/X ofthe voltage differential on the switching control signal. By couplingdifferent control signals though different valued capacitors, eachcontrol signal may effect a different bias on the complementary node towhich it is connected.

Rather than relying on the initial voltage, other PUFs may rely onvariations in overall path delays. Examples of delay-dependent PUFsinclude arbiter PUFs, such as the arbiter PUF shown in FIG. 1, and ringoscillator PUFs, such as the ring oscillator PUF shown in FIG. 2. Forsuch delay-dependent PUFs, the systems and methods of the presentdisclosure use control signals to bias the delays through one or morepaths. In some embodiments, the control signals couple additionalparasitic loading onto one or more nodes that comprise the one or morethe paths. A delay-dependent PUF in accordance with the presentdisclosure is shown in FIG. 11.

The present disclosure enhances the ability to measure the margin of aresponse bit for a PUF by adding one or more bias control signals thatbias the response of one or more PUF response bits. As an illustrativeexample and with no loss in generality, when a bias control signal isasserted, a PUF bit will be slightly more likely to be read as a 1 thanwhen the bias control signal is not asserted. These bias control signalsmay be static (level-sensitive) or dynamic (edge-sensitive). Inparticular, static bias control signals may be applied to delay-basedPUF cells, such as that shown in FIG. 11, and dynamic bias controlsignals may be applied to voltage-based PUF cells, such as those shownin FIGS. 8 and 9.

FIGS. 1 and 2 show two example block diagrams of known delay-based PUFs.In particular, FIG. 1 shows a block diagram of an arbiter PUF circuit100, which includes a set 102 of twelve multiplexers and an arbiter 104.The left side of the arbiter PUF circuit 100 receives a rising signal,which splits into two paths and travels toward the right side of thecircuit 100. The arbiter PUF circuit 100 also receives a six-bitchallenge input C[1:6] and computes an output based on a relative delaydifference between the two paths. The challenge input bits C[1:6] areused to control the routing multiplexers on the two paths withostensibly equal delays. The challenge input bits C[1:6] control pairsof multiplexers of the set 102 to select whether or not to switch thetop and bottom signals when passing two delay signals. In particular,when a challenge input bit is 0, the corresponding pair of multiplexersin the set 102 pass through the two delay signals without switching thetop and bottom signals. Alternatively, when a challenge input bit is 1,the top and bottom signals are switched before being passed through thecorresponding pair of multiplexers.

Manufacturing variations in the multiplexers in the set 102 and linedrivers cause the two paths to have different delays that depend on thepath specified by the challenge input bits. By selectively switching andpassing the top and bottom signals, different sets of challenge inputbits C[1:6] will give rise to different delay paths. The first path toreach the arbiter 104, which includes a set/reset latch composed of twocross-coupled NOR gates causes either a 1 or a 0 to be latched.

FIG. 2 shows a block diagram of a ring oscillator PUF circuit 200, inaccordance with the prior art. The ring oscillator PUF circuit 200includes a first ring oscillator 216, a second ring oscillator 218, anda counter circuit 214. The delay of the ring oscillator PUF circuit 200is controlled by a set of six challenge input bits C[1:6], which areprovided as control signals to a set of twelve multiplexers 212, six ofwhich are included in the first ring oscillator 216, and six of whichare included in the second ring oscillator 218. The first ringoscillator 216 and the second ring oscillator 218 include loops thatoscillate at certain frequencies. The loops drive the two counters inthe counter circuit 214 in FIG. 2, which is used to produce responsebits to a particular challenge. In particular, after the second ringoscillator 218 has completed a fixed number N of cycles, the first ringoscillator 216 is latched. Depending on the differences in delay inbetween the two ring oscillators 216 and 218, the first ring oscillator216 may take more or fewer cycles than the second ring oscillator 218.The number of cycles taken by the first ring oscillator is used as thePUF response.

While FIGS. 1 and 2 show examples of known delay-based PUF circuits,FIGS. 3-5 show voltage-based PUF circuits according various embodimentsof the present disclosure. FIG. 3 shows a block diagram of a balancedbutterfly PUF circuit 300, in accordance with some embodiments of thepresent disclosure. The butterfly PUF circuit 300 includes twocross-coupled level sensitive latches 320 and 322. Both latches 320 and322 may be permanently enabled such that the latches 320 and 322 are ina flow-through mode. In this case, during initialization, one latch isasynchronously cleared to 0 while the other latch is asynchronously setto 1. In accordance with the present disclosure, the complementary nodesof the balanced butterfly PUF circuit 300 are labeled N+ and N−. Whenthe “init” signal 324 becomes non-asserted, the cross-coupled latches320 and 322 settle into either a 00 state or a 11 state, depending onmanufacturing variations and initial conditions on the N+ and N− nodes.

FIG. 4 shows a block diagram of a logic-based butterfly PUF circuit 400,in accordance with some embodiments of the present disclosure. Thelogic-based butterfly PUF circuit 400 includes two NOR gates 430 and432, and the complementary nodes of the balanced PUF are labeled N+ andN−. As shown in FIG. 4, the logic-based butterfly PUF circuit 400 isimplemented using two NOR gates 430 and 432, but in general alogic-based balanced PUF may be implemented using any type or number oflogic devices.

FIG. 5 shows a block diagram of a balanced SRAM bit cell 500, inaccordance with some embodiments of the present disclosure. The balancedSRAM bit cell 500 includes six transistors 540, 542, 544, 546, 548, and550. The four transistors 540, 542, 544, and 546 form two cross-coupledinverters. The complementary nodes of the balanced SRAM cell 500 arelabeled N+ and N−.

FIG. 6 shows a block diagram of a matrix of known SRAM bit cells 600. Inparticular, each of the (N+1)×(N+1) SRAM bit cells in the matrixincludes six transistors and may be equivalent to the SRAM bit cell 500shown in FIG. 5.

FIG. 7 shows a block diagram of a balanced PUF bit cell 700, inaccordance with some embodiments of the present disclosure. The outputof the PUF bit cell 700 depends at least partially on the initialvoltage level at the complementary nodes N− and node N+. The PUF bitcell 700 is a generalized balanced cell that may represent any of thebalanced circuits shown and described in relation to any of the circuitsshown in FIGS. 3-5.

FIG. 8 shows a block diagram 800 of a balanced PUF bit cell 882 and abias control circuit 884 including six bias control lines 870, 872, 874,876, 878, and 880, in accordance with some embodiments of the presentdisclosure. The complementary nodes of the balanced PUF bit cell 882 areconnected via coupling capacitors C[1:3]+ and C[1:3]− to bias controllines BIAS[1:3]+ (shown as bias control lines 870, 874, and 878 in FIG.8) and BIAS[1:3]− (shown as bias control lines 872, 876, and 880)respectively. The +/− suffixes for the coupling capacitors and the biascontrol lines specify whether the capacitor or control signal biases theN+ node or the N− node of the balanced PUF bit cell 882. The capacitorsC0− and C0+ may represent the overall parasitic or other staticcapacitances on the N− and N+ nodes that are not controlled by any ofthe bias control signals.

As shown in FIG. 8, the capacitances of the various coupling capacitorsvary for the different stages of capacitors. The largest pair ofcoupling capacitors C1− and C1+ may have capacitances that are ¼ of theoverall parasitic capacitances C0− and C0+. The other pairs of couplingcapacitors may have capacitances that sequentially decrease by a factorof 2× at each stage, such that C2− and C2+ have capacitances that are ⅛of the capacitances C0− and C0+, and C3− and C3+ have capacitances thatare 1/16 of the capacitances C0− and C0+. The capacitors and biascontrol signals 870, 872, 874, 876, 878, and 880 shown in block diagram800 are shown for illustrative purposes only, and one of ordinary skillin the art will understand that any number of capacitors with any set ofcapacitances may be used without departing from the scope of the presentdisclosure.

In the example shown in FIG. 8, six bias control signals 870, 872, 874,876, 878, and 880 are shown. Sequentially asserting additional biascontrol signals will cause the response bit to become progressively morelikely to be read as a 1 (or a 0). The degree of bias that each biascontrol signal has over the response bit may be the same or may differ.In order to effect a different degree of bias for each bias controlsignal, the bias control signals may be ordered such that each biascontrol signal has twice the biasing effect of the prior bias controlsignal, for example. In this case, the amount of bias may be fine-tunedby applying a binary value to the bias-control signals. In general,other ratios, such as 0.5×, 1.5×, 3×, 4×, 5×, or any other suitableratio, may be used. Moreover, the change in biasing effect acrossconsecutive bias control signals may be the same or different withoutdeparting from the scope of the present disclosure.

In FIG. 8, only one PUF bit response cell is shown. In general, the biascontrol signals in FIG. 8 may be used to apply bias control signals toany number of PUF bits simultaneously or sequentially. When it isdesirable to apply bias control signals to an array of PUF bits (e.g., atwo-dimensional array), polarity control signals may be applied todifferent PUF bits in the array to change the polarity of the biascontrol signals that are applied to each PUF bit. For example, it may bedesirable to apply positive bias control signals to bits in an arraythat have a nominal response of 0 and negative bias control signals tobits in the array that have a nominal response of 1. In this case,selectively asserting a set of polarity control signals may allow forthe use of a single set of bias control signals to be applied to all thebits in the array.

FIG. 9 shows a block diagram 900 of a balanced PUF bit cell 982 and abias control circuit 984 that includes six bias control lines 970, 972,974, 976, 978, and 980, in accordance with some embodiments of thepresent disclosure. Similar to the block diagram 800 shown in FIG. 8,the complementary nodes of the balanced PUF bit cell 982 are connectedvia coupling capacitors C[1:3]+ and C[1:3]− to bias control linesBIAS[1:3]+ (shown as bias control lines 970, 974, and 978 in FIG. 9) andBIAS[1:3]− (shown as bias control lines 972, 976, and 980) respectively.The +/− suffixes for the coupling capacitors and the bias control linesspecify whether the capacitor or control signal biases the N+ node orthe N− node of the balanced PUF bit cell 982. The capacitors C0− and C0+may represent the overall parasitic or other static capacitances on theN− and N+ nodes that are not controlled by any of the bias controlsignals.

FIG. 9 is similar to the block diagram 800 shown in FIG. 8, except thatFIG. 9 includes a polarity control block 986. In FIG. 9, the effects ofthe bias control signals 970, 972, 974, 976, 978, and 980 are modifiedby a polarity control signal, which is controlled by the initial outputof the balanced PUF bit cell 982 and provides a control signal to sixmultiplexers. When the polarity control signal is asserted (i.e., whenthe control signal is a 1), the meaning of the bias control signalsBIAS[1:3]+ and BIAS[1:3]− signals are reversed. Specifically, biascontrol signals 970 and 972 are reversed, bias control signals 974 and976 are reversed, and bias control signals 978 and 980 are reversed.When the bias control signals are reversed in this manner, asserting thepositive bias control lines 970, 974, and 978 may cause the PUF bit cellto be more likely to settle to a value of 0 rather than 1, and assertingthe negative bias control lines 972, 976, and 980 may cause the PUF bitcell to be more likely to settle to a value of 1 rather than a value of0. Otherwise, when the polarity control signal is not asserted (i.e.,when the control signal is a 0), bias control signals are not reversed,and the behavior of the circuit shown in FIG. 9 is the same as thecircuit shown in FIG. 8.

With the use of polarity control block 986, the nominal value of thecorresponding response bit may be latched onto the polarity controlline, such that asserting further bias control signals would bias thereading of that response bit away from its nominally read value. Inother words, a positive bias may be applied if the nominal response bitvalue was a 0, and a negative bias may be applied if the nominalresponse bit value was a 1.

Even though only one PUF bit response cell is shown in FIG. 9, the biascontrol signals 970, 972, 974, 976, 978, and 980 may be used to applybias control signals to any number of PUF bits simultaneously orsequentially. When it is desirable to apply bias control signals to anarray of PUF bits, polarity control blocks such as polarity controlblock 986 may be applied to different PUF bits in the array to changethe polarity of the bias control signals that are applied to each PUFbit. The use of polarity control block 986 allows the bias controlsignal circuitry in a PUF bit cell array to be efficient so thatdifferent bias control signals do not need to be applied to differentPUF bits. In this way, polarity control allows the circuitry to savespace and make use of the same set of bias control signals for an arrayof PUF bits, even if it is desirable to apply different polarities ofthe bias control signals to the PUF bits in the array.

FIG. 10 shows an example of the various voltage levels at four biascontrol lines and at two complementary nodes N− and N+, in accordancewith some embodiments of the present disclosure. In the example of FIG.10, the negative bias control lines BIAS1− and BIAS2− are initialized toa ground voltage (GND), the positive bias control lines BIAS1+ andBIAS2+ are initialized to a positive voltage V_(CC), which may be the DCvoltage from a power supply that is applied to a collector of atransistor. Similarly, the complementary nodes are both initialized toV_(CC). When the bias control line BIAS1− has a voltage change from GNDto V_(CC) at time 1090, a lower positive voltage change is coupled tothe complementary node N−, biasing the node N− to a value slightly aboveV_(CC). At time 1091, the bias control line BIAS1+ has a voltage changefrom V_(CC) to GND, which causes the node N+ to become slightly biasedbelow V_(CC).

Subsequently, when the other bias control signals BIAS2− and BIAS2+ havevoltage changes at times 1092 and 1093, respectively, this applieslarger voltage changes to nodes N− and N+ than when BIAS1− and BIAS1+had voltage changes at times 1090 and 1091. In particular, at time 1092,the BIAS2− control signal has a voltage change from GND to V_(CC), whichcauses the node N− to have a larger increase in voltage than theincrease that occurred at time 1090. Similarly, at time 1093, the BIAS2+control signal has a voltage change from V_(CC) to GND, which causes thenode N+ to have a larger decrease in voltage than the decrease thatoccurred at time 1092. This is because the BIAS2− and BIAS2+ controlsignals may have a larger capacitive coupling than the capacitivecoupling of the BIAS1− and BIAS1+ control signals.

The voltage changes effected on the nodes N− and N+ that take place attimes 1094, 1095, 1096, and 1097 mirror those that took place at times1090, 1091, 1092, and 1093. In particular, the voltage changes affectedon the complementary nodes N− and N+ that originated from voltagechanges in the BIAS1− and BIAS1+ control signals are smaller than thosethat originated from voltage changes in the BIAS2− and BIAS2+ controlsignals.

As is described in relation to FIGS. 8 and 9, PUFs may be implementedbased on voltages. In such cases, the systems and methods of the presentdisclosure may include coupling one or more capacitors to each of thecomplementary nodes and to different bias control lines, such thatchanging the voltage on the bias control line may change the voltage onthe complementary node. The block diagrams of FIGS. 8 and 9 are shown asillustrative examples only, and one of ordinary skill in the art thatany bias control circuitry that adjusts the voltages of thecomplementary nodes N− and N+ may be used without departing from thescope of the present disclosure. In one example, a voltage may beapplied to the silicon in which one or more transistors reside, therebyusing the body effect of the one or more transistors to give rise tochanges in the voltages of the complementary nodes.

Rather than relying on voltages, other PUFs may rely on variations inoverall path delays. For such delay-dependent PUFs, such as those shownin FIGS. 1 and 2, the systems and methods of the present disclosure usecontrol signals to bias the delays through one or more paths. In someembodiments, the control signals add or remove additional parasiticloading onto the one or more the paths to cause or remove additionaldelays.

FIG. 11 shows a block diagram of bias circuitry 1100 for a delay-basedPUF bit cell, in accordance with some embodiments of the presentdisclosure. The bias circuitry 1100 may be used in relation with anarbiter PUF such as the arbiter PUF circuit 100 shown in FIG. 1. Asshown in FIG. 11, four load capacitors C1−, C1+, C2−, and C2+ providecapacitive loading, which may or may not be added to one or more of thedelay paths by asserting one or more of the bias control signals 1101,1102, 1103, and 1104. In particular, each of the bias control signals1101, 1102, 1103, and 1104 is used to connect one terminal of a loadcapacitor C1−, C1+, C2−, and C2+ to one of the nodes along a delay path,and the other terminal of the load capacitor is tied to another node (asshown in FIG. 11, GND).

When any of the bias control signals 1101, 1102, 1103, and 1104 isasserted, the path through the node connected to the source of the passgate that is controlled by that bias control signal is marginally sloweddown, thereby increasing the delay of the corresponding path. In thisway, the presence of the load capacitors and the bias control signalsallows for enhanced control of the delays along the paths. Any number ofbias control signals may be used to control any number of pass gatesthat are connected to load capacitors having the same or differentcapacitances. In one example, the C2+ and C2− load capacitors may havetwice the capacitance as the C1+ and C1− capacitors. The capacitors C0+and C0− represent the total parasitic capacitance on the complementarypath nodes.

As is shown in FIG. 11, the coupling is performed using a passtransistor (or a complementary pair of pass transistors) whose gates arecontrolled (directly or indirectly) by the control signals, whose one ormore sources are connected to one of the path nodes, and whose one ormore drains are connected to a terminal of a capacitor, with the otherterminal of the capacitor being tied to V_(CC), GND, or another pathnode. However, in general, other implementations are possible, such asby changing the drive strengths of the path node drivers, or changingthe power supply voltage for the path node drivers. In one example,multiplexers or any type of delay element may be added along the pathlines to add incremental delays paths. In one example, a voltage may beapplied to the silicon in which one or more transistors reside, usingthe body effect of the one or more transistors to give rise toadditional delays. In general, one of ordinary skill in the art willunderstand that any suitable circuitry or method may be applied tosystematically introduce or remove delays along any number of delaypaths in a bias circuitry for a delay-based PUF cell without departingfrom the scope of the present disclosure.

FIG. 12 shows an illustrative flow diagram of a process 1200 forimproving the stability of an array of PUF cells, in accordance withsome embodiments of the present disclosure. In particular, FIG. 12illustrates the application of a bias control circuit for performingmargin testing on an array of PUF cells.

At 1202, one or more bias control signals are applied to a plurality ofPUF cells. As described in relation to FIGS. 8 and 9, when the PUF cellis based on voltage, a bias control circuit may include a set ofcapacitors. Each capacitor may couple a node of the PUF cell and one ofthe bias control signals, such that the voltage applied to the biascontrol signal has an effect on the voltage at the node of the PUF cell.In this case, the PUF cell may be a butterfly PUF cell (as shown in FIG.3 or 4) or an SRAM PUF cell (as shown in FIG. 5).

As described in relation to FIG. 11, when the PUF cell is based ondelay, a bias control circuit may include a set of transistors and loadcapacitors that affect the delay of the PUF cell. In this case, the PUFcell may be an arbiter PUF cell (as shown in FIG. 1) or a ringeroscillator PUF cell (as shown in FIG. 2).

In some embodiments, the one or more bias control signals are modifiedbefore being applied to the plurality of PUF cells. In particular, apolarity control signal may be selectively applied for each of the oneor more bias control signals. The polarity control signals mayselectively change the polarity of each bias control signal that isapplied to the PUF cells. As an example, the polarities that areselected for applying to the bias control signals may be based on thenominal responses of the PUF cells. In particular, when the nominalresponse of a PUF cell is 1, the polarity of the bias control signal maybe selected so as to apply a negative bias to the PUF cell. Similarly,when the nominal response of a PUF cell is 0, the polarity of the biascontrol signal may be selected so as to apply a positive bias to the PUFcell. Selecting the polarities of the bias control signals in this wayallows for marginal testing of the PUF cells, to identify PUF cells thatmay flip (or otherwise change) their responses away from the nominalresponses.

At 1204, any PUF cells that have changed outputs in response to the biascontrol signals are identified, and at 1206, stabilities of the PUFcells are assessed based on whether the outputs of the PUF cells arechanged. When a PUF cell has a flipped response when the bias controlsignals are applied, this may be a sign that the flipped PUF cell isunstable.

In some embodiments, an array of PUF cells includes more PUF cells thanare needed for an application. In other words, an array of PUF cellscontains M PUF cells, but only N PUF cells are necessary for anencryption, for example, where N<M. It may be desirable to identify themost stable subset of PUF cells in the array. In this case, when a PUFcell flips in response to an application of bias control signals to thePUF cell, the flipped PUF cell may be labeled as “unstable” and may beeliminated. The bias control signals may be adjusted to further test themargins of the remaining PUF cells (i.e., applying positive bias tothose PUF cells with nominal response 0 and applying negative bias tothose PUF cells with nominal response 1), and any of the remaining PUFcells that flip in response to the adjusted bias control signals mayalso be eliminated. This process may be iteratively repeated until N PUFcells remain. The remaining N PUF cells may be identified as the N moststable PUF cells out of the M PUF cells in the array.

The stability of a PUF cell may be assessed based on any number offactors. In one example, a PUF cell that does not flip even whendifferent bias controls are applied may be labeled as stable. In anotherexample, a PUF cell that flips the least often compared to other PUFcells may be labeled as stable. In another example, a PUF cell thatrequires the greatest magnitude bias control signals to flip may belabeled as stable. In another example, if N PUF cells are required foran application, the N/2 most stable PUF cells with nominal response 1and the N/2 most stable PUF cells with nominal response 0 are selectedas the stable set. In this case, a PUF cell with a nominally read 1 maybe selected over an otherwise more stable PUF cell with a nominally read0 (or vice versa). These examples are for illustrative purposes only,and one of ordinary skill in the art will understand that anycombination of the methods described herein for determining stability,or any other suitable method for determining stability of a PUF cell,may be used without departing from the scope of the present disclosure.

In some embodiments, the bias control signals are swept over some range,and the PUF response bit values are read one or more times for each ofthe different bias settings. In particular, the nominally read 1 PUFcells may be read under various degrees of negative bias, and thenominally read 0 PUF cells may be read under various degrees of positivebias. In some embodiments, the number of PUF responses read for each ofthe different bias settings may be the same. Moreover, the number ofused negative bias settings and the number of used positive biassettings may be the same. In some embodiments, for each positive biassetting that results in a particular positive bias value, a negativebias setting may be used that results in a negative bias value of thesame magnitude as the corresponding positive bias value.

At 1208, a subset of the plurality of PUF cells is selected based on therespective stabilities. As an example, selecting the subset of theplurality of PUF cells may include selecting a predetermined number(i.e., N) of PUF cells in the plurality of PUF cells with the higheststabilities. In general, the selected subset of PUF cells may beselected based on the satisfaction of one or more criteria. The criteriamay include identifying at least N PUF cells that are associated withstability scores that exceed some threshold. As an example, thestability score of a PUF cell may correspond to the smallest magnitudeof the bias control signal that was required to cause the PUF cell toflip. As another example, the stability score of a PUF cell maycorrespond to a frequency at which the PUF cell flips in response tovarious bias control signals.

In some embodiments, when N PUF cells are required for an application,the N most stable PUF cells are selected, and helper data is used tomask out the remaining less stable bits.

The foregoing is merely illustrative of the principles of theembodiments and various modifications can be made by those skilled inthe art without departing from the scope and spirit of the embodimentsdisclosed herein. The above described embodiments of the presentdisclosure are presented for purposes of illustration and not oflimitation, and the present invention is limited only by the claimswhich follow.

What is claimed is:
 1. An apparatus for identifying stable physicallyunclonable function (PUF) cells, the apparatus comprising: an array ofPUF cells; a bias control circuit having a plurality of bias controllines, wherein the bias control lines apply one or more bias controlsignals to each PUF cell in the array of PUF cells; and a selectorcircuit that selects a subset of the PUF cells in the array of PUF cellsbased on whether outputs of the PUF cells in the array of PUF cellschange in response to application of the bias control signals.
 2. Theapparatus of claim 1, wherein the bias control circuit includes at leastone capacitor coupling a node of a PUF cell in the array of PUF cellsand one of the one or more bias control signals.
 3. The apparatus ofclaim 1, wherein each PUF cell in the array of PUF cells is based on avoltage and is a butterfly PUF cell or a SRAM PUF cell.
 4. The apparatusof claim 1, wherein the bias control circuit includes at least atransistor connected to a load capacitor such that when the transistoris disabled, the load capacitor is disconnected from a delay path for aPUF cell in the array of PUF cells.
 5. The apparatus of claim 1, whereineach PUF cell in the array of PUF cells is based on a delay and is anarbiter PUF cell or a ring oscillator PUF cell.
 6. The apparatus ofclaim 1, further comprising a polarity control circuit that selectivelychanges a polarity of at least one bias control signal before the one ormore bias control signals are applied to each PUF cell in the array ofPUF cells.
 7. The apparatus of claim 1, wherein a first PUF cell thathas a changed output when the one or more bias control signals areapplied to the first PUF cell is less stable than a second PUF cell thathas an unchanged output when the one or more bias control signals areapplied to the second PUF cell.
 8. The apparatus of claim 1, wherein theselector circuit selects the subset of PUF cells by selecting apredetermined number of PUF cells in the array of PUF cells that aremore stable than a remainder of the PUF cells in the array of PUF cells.9. A circuit for measuring a stability of a physically unclonablefunction (PUF) cell, the circuit comprising: a bias control circuitryhaving a plurality of bias control lines, wherein: each bias controlline applies a bias control signal to the PUF cell; and the stability ofthe PUF cell is evaluated based on whether an output of the PUF cellchanges in response to application of the bias control signals to thePUF cell.
 10. The circuit of claim 9, wherein the bias control circuitryincludes at least one capacitor coupling a node of the PUF cell and oneof the plurality of bias control signals.
 11. The circuit of claim 9,wherein the PUF cell is based on a voltage and is a butterfly PUF cellor a SRAM PUF cell.
 12. The circuit of claim 9, wherein the bias controlcircuitry includes at least a transistor connected to a load capacitorsuch that when the transistor is disabled, the load capacitor isdisconnected from a delay path for a PUF cell in the array of PUF cells.13. The circuit of claim 9, wherein the PUF cell is based on a delay andis an arbiter PUF cell or a ring oscillator PUF cell.
 14. The circuit ofclaim 9, further comprising a polarity control block that selectivelychanges a polarity of the plurality of bias control lines before theplurality of bias control signals are applied to the PUF cell.
 15. Thecircuit of claim 9, wherein the PUF cell is unstable when the output ofthe PUF cell changes in response to the application of the bias controlsignals to the PUF cell, and the PUF cell is stable when the output ofthe PUF cell is unchanged in response to the application of the biascontrol signals to the PUF cell.
 16. A method for identifying stablephysically unclonable function (PUF) cells, the method comprising:applying one or more bias control signals to a plurality of PUF cells;identifying any PUF cells that have a changed output in response to theone or more bias control signals; assessing stabilities of the PUF cellsbased on whether the outputs of the PUF cells change; and selecting asubset of the plurality of PUF cells based on the respectivestabilities.
 17. The method of claim 16, wherein selecting the subset ofthe plurality of PUF cells comprises selecting a predetermined number ofPUF cells in the plurality of PUF cells with higher stabilities than aremainder of the PUF cells in the plurality of PUF cells.
 18. The methodof claim 16, further comprising applying a polarity control signal foreach bias control signal to selectively change the polarity of each biascontrol signal that is applied to the plurality of PUF cells.
 19. Themethod of claim 16, further comprising selecting one or more polaritiesfor the one or more bias control signals based on a nominal response ofthe PUF cells.
 20. The method of claim 16, wherein a PUF cell in theplurality of PUF cells is unstable when the output of the PUF cellchanges in response to the one or more bias control signals, and the PUFcell in the plurality of PUF cells is stable when the output of the PUFcell is unchanged in response to the one or more bias control signals.